Encyclopedias will tell you that the fall of Jerusalem to Babylon happened in 586/87.
http://en.wikipedia.org/wiki/Babylonian_captivity
"The Babylonian captivity, or Babylonian exile, was the period in Jewish history from the deportation and exile of Jews of the ancient Kingdom of Judah to Babylon by Nebuchadnezzar II starting with the first deportation in 597 BC of the royal court and other prominent citizens and craftsmen, along with a sizable portion of the Jewish population of Judah, numbering about 10,000, and continuing even after the fall of Jerusalem and destruction of the Temple in 587 BCE. [ 2 ] The forced exile lasted until the fall in 538 BCE of Babylon to the Persian Cyrus the Great, who gave Jews permission to return to Yehud Province. [ 3 ] However, Jews continued to live in Babylon until the establishment of Israel in the mid-20th century CE, when most of them moved to Israel.
The captivity and subsequent return to Israel and rebuilding of the Jerusalem Temple are pivotal events in the history of the Jews and Judaism, and had a far-reaching impact on the development of Jewish culture and practices."